A cylinder has inner and outer radii of $9 c m$ $9 cm$ and $16 c m$ $16 cm$ , respectively, and a mass of $4 k g$ $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $10 H z$ $10 Hz$ to $15 H z$ $15 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-02-16T15:22:36

The change in angular momentum is $= 2.122 .12 k g m^{2} s^{- 1}$ $=2.122.12kgm^2s^(-1)$

The angular momentum is $L = I ω$ $L=Iomega$

where $I$ $I$ is the moment of inertia

The change in angular momentum is

$Delta L=I*Delta omega$

For a cylinder, $I=m(r_1^2+r_2^2)/2$

$Delta omega =(15-10)*2pi=(10 pi )rads^-1$

So, $I=4*(0.09^2+0.16^2)/2=0.0674kgm^2$

$L=10pi*0.0674=2.12kgm^2s^(-1)$

A cylinder has inner and outer radii of 9 cm9cm9 cm and 16 cm16cm16 cm, respectively, and a mass of 4 kg4kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 10 Hz10Hz10 Hz to 15 Hz15Hz15 Hz, by how much does its angular momentum change?